Two point like charges `Q_(1)` and `Q_(2)` are positioned at point 1 and 2. The firld intensity to the right of the chaege `Q_(2)` on the line that passes through the two charges varies accoreing to a law that is represented schematically in fig. The field intensity is assumed to be positive if its direction coincides with the positive direction on the x-axis. The distance between the charges is l.

The ratio of the absolute values of the charges `|Q_(1)//Q_(2)|` is

Answer

A, B, C

Explanation

Over charge `Q_2` field intensity is infinite along negatve `x` -axis. Therefore `Q_2` is negative.
Beyon `xgt(l+a)`, field intensity is positive. Therefore `Q_1` is positive
b. At `x=l+a`, field intensity is zero.
`:. (kQ_1)/((l+a)^2)=(kQ_2)/a^2` or `|Q_1/Q_2|=((l+a)/a)^2`
c. Intensity at distance `x` from charge `2` would be
`E=(kQ_1)/((x+l)^2-(kQ_2)/x^2`
For `E` to be maximum `(dE)/(dx)=0`
or `-(2kQ_1)/((x+l)^3)+(2kQ_2)/x^3=0`
or `(1+l/x)^3=Q_1/Q_2=((l+a)/a)^2`
or `1+l/x=((l+a)/a)^(2//3))`
or 1+l/x=((l+a)/a)^(2//3)`
or `x=l/(((l+a)/a)^(2//3)-1)`
or `b=l/(((l+1)/a)^(2//3)-1)`